where constraint \(({\rm C1})\)  relates to the average TX power at node \(k\)  and constraint \(({\rm C2})\)  refers to the hardware capabilities of the analog canceller. Constraint \(({\rm C3})\)  imposes the threshold \(\rho _{\rm A}\in \mbox{$\mathbb {R}$}\)  on the average power of the residual SI signal after analog cancellation and analog TX/RX beamforming. Finally, constraint \(({\rm C4})\)  refers to the predefined TX and RX beam codebooks. To tackle \(\mathcal {OP}\) , which is a nonconvex problem with nonconvex constraints, we adopt a similar to [1]} decoupled way that in this case requires at most \(\alpha _{\max }\triangleq N_{k}^{(\mathrm {RF})}-1\)  iterations including closed form expressions for the design parameters. We first solve for \(k\) , \(k^{(\mathrm {RF})}\) , \(k^{(\mathrm {BB})}\) , and \(\mathbf {U}_k^{(\mathrm {RF})}\)  maximizing the DL rate, and then find \(\mathbf {U}_k^{(\mathrm {BB})}\)  maximizing the UL rate. Specifically, we formulate the following optimization subproblem for the design of \(k\) , \(k^{(\mathrm {RF})}\) , \(k^{(\mathrm {BB})}\) , and \(\mathbf {U}_k^{(\mathrm {RF})}\) :
\(\begin{split}\mathcal {OP}1: &\max _{k,k^{(\mathrm {RF})},k^{(\mathrm {BB})},\mathbf {U}_k^{(\mathrm {RF})}} \mathcal {R}_{\rm DL}~~\textrm {s.t.}~~({\rm C1}),\,({\rm C2}),\,\text{and}\,({\rm C3}).\end{split}\) 
